Revista Matemática Iberoamericana


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Published online first: 2020-10-26
DOI: 10.4171/rmi/1228

Totally geodesic submanifolds of Damek–Ricci spaces

Sinhwi Kim[1], Yuri Nikolayevsky[2] and JeongHyeong Park[3]

(1) Sungkyunkwan University, Suwon, Republic of Korea
(2) La Trobe University, Melbourne, Australia
(3) Sungkyunkwan University, Suwon, Republic of Korea

We classify totally geodesic submanifolds of Damek–Ricci spaces and show that they are either subgroups (“smaller” Damek–Ricci spaces) or isometric to rank-one symmetric spaces of negative curvature.

Keywords: Totally geodesic submanifold, Damek–Ricci space

Kim Sinhwi, Nikolayevsky Yuri, Park JeongHyeong: Totally geodesic submanifolds of Damek–Ricci spaces. Rev. Mat. Iberoam. Electronically published on October 26, 2020. doi: 10.4171/rmi/1228 (to appear in print)